Ant Colony Optimization EDWIN WONG PHILLIP SUMMERS ROSALYN KU - - PDF document
Ant Colony Optimization EDWIN WONG PHILLIP SUMMERS ROSALYN KU PATRICK XIE PIC 10C SPRING 2011 Swarm Intelligence Swarms Swarm of bees Ant colony as swarm of ants Flock of birds as swarm of birds Traffic as swarm of cars
EDWIN WONG PHILLIP SUMMERS ROSALYN KU PATRICK XIE PIC 10C SPRING 2011
Swarm of bees Ant colony as swarm of ants Flock of birds as swarm of birds Traffic as swarm of cars Immune system as swarm of cells
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Model complex behavior using simple agents
Idea: stigmergy is a mechanism of communication by modifying the
Example Take some dirt in your mouth Moisten it with pheromones Walk in the direction of the strongest pheromone concentration Drop what you are carrying where the smell is the strongest Ant Colony Optimization uses artificial stigmergy
Marco Dorigo (1991) – PhD thesis Technique for solving problems which can be expressed as finding
Each ant tries to find a route between its nest and a food source
Wander randomly at first, laying down a pheromone trail If food is found, return to the nest laying down a pheromone trail If pheromone is found, with some increased probability follow the
Once back at the nest, go out again in search of food
However, pheromones evaporate over
2.
3.
To design technical systems for
NOT to design an accurate model of
Nature Computer Science Natural habitat Graph (nodes and edges) Nest and food Nodes in the graph: start and destination Ants Agents, our artificial ants Visibility The reciprocal of distance, η Pheromones Artificial pheromones ,τ Foraging behavior Random walk through graph (guided by pheromones)
Scheme:
Construct ant solutions Define attractiveness τ, based on experience from previous solutions Define specific visibility function, η, for a given problem (e.g. distance)
Ant walk
Initialize ants and nodes (states) Choose next edge probabilistically according to the attractiveness and visibility
Update attractiveness of an edge according to the number of ants that pass
through
ρ small low evaporation slow adaptation ρ large high evaporation fast adaptation
(e.g. ) Q/length of tour
choose probabilistically (based on previous equation) the next state to move into;
Example: black box, cracking a combination lock, planning a route
In the Traveling Salesman Problem (TSP) a salesman visits n cities
Problem: What is the shortest possible route?
Create permutations for all N cities
Iteratively check all distances Can you guys figure out the Big O
Searches for locally optimal solutions
inverse distance (visibility) between cities
τ = (1- ρ) * τ + Δτk Δτk = Q/Lk , Q is constant, Lk is the length of tour of ant k
Pseudocode: initialize all edges to (small) initial pheromone level τ0; place each ant on a randomly chosen city; for each iteration do: do while each ant has not completed its tour: for each ant do: move ant to next city by the probability function end; end; for each ant with a complete tour do: evaporate pheromones; apply pheromone update; if (ant k’s tour is shorter than the global solution) update global solution to ant k’s tour end; end;
Allows a balance between using previous knowledge and exploring new
solutions
Limited to problems that can be simulated by graphs and optimized Coding difficulties for different problems
This allows for faster convergence As we construct more and more solutions, there is more
Pseudo-random proportion rule: at each decision point for an ant, it has a probability (1-q0) of using the
same probability function as in the Ant System or q0 of picking the best next node based on previous solutions
Global Trail Update: only the
Local Trail Update: all ants
Both the global solution and each ant update their edges with
Routing problems Urban transportation systems Facility placement Scheduling problems
Vary the importance of
pheromone
Play around with evaporation rate Add time constraint Add obstacles
Urban solid waste collection Traffic flow optimization